latent activation modeling

Block-structured latent variable models are widely employed in psychology, education, economics, and genetics, yet their identifiability and estimation performance have long lacked a systematic theoretical foundation. This work establishes, for the first time, identifiability conditions for such models under various block designs and introduces a Lagrangian-type nonconvex optimization framework based on constrained maximum likelihood estimation. The study derives both non-asymptotic error bounds and asymptotic distributions for the resulting estimators. The proposed algorithm enjoys strong theoretical guarantees and, as demonstrated through extensive simulations and empirical analyses, efficiently and accurately estimates latent variable models across diverse block structures.

This work addresses the fragmentation between classical probabilistic latent variable models (PLVMs) and modern generative AI methods by unifying their underlying modeling principles, contrasting inference strategies, and analyzing representational trade-offs. We propose a unified probabilistic latent variable framework that systematically integrates seven canonical models: probabilistic PCA, hidden Markov models, variational autoencoders, normalizing flows, diffusion models, autoregressive models, and generative adversarial networks. Through formal analysis of their latent structures, inference mechanisms, and generative pathways, we construct the first theoretical taxonomy of generative AI. This framework clarifies the methodological evolution of generative modeling, strengthens its theoretical foundations, and provides interpretable conceptual guidance and structured design principles for developing novel architectures. (149 words)

This work addresses the tractability of exact inference and learning in exponential-family latent variable models (LVMs), seeking to characterize the precise boundary of models admitting closed-form analytical solutions without approximation. Method: We derive necessary and sufficient conditions for prior–posterior conjugacy in exponential-family LVMs, providing the first systematic characterization of exact solvability. We further propose a composable graphical model construction framework that preserves structural flexibility while guaranteeing analytic tractability throughout. A general-purpose exact Bayesian inference and parameter learning algorithm is developed, accompanied by an open-source implementation supporting empirical validation across diverse models. Contribution/Results: Our results substantially broaden the class of LVMs amenable to exact inference—bypassing variational approximations or Monte Carlo sampling—and establish a rigorous theoretical foundation and practical toolkit for interpretable, high-precision latent-variable modeling.

Unsupervised interpretable learning for high-dimensional natural data (e.g., images) remains challenging due to the lack of identifiable, semantically meaningful representations. Method: This paper models semantic concepts as discrete implicit causal variables and constructs an identifiable multilevel causal hierarchy. It formally defines discrete concepts as hierarchical causal latent variables and establishes novel identifiability conditions for continuous high-dimensional observations—enabling complex causal structures beyond trees and DAGs. The approach integrates causal representation learning, hierarchical latent modeling, identifiability analysis, and latent diffusion mechanisms. Contributions/Results: We theoretically prove identifiability of intricate hierarchical concepts under unsupervised learning. Synthetic experiments validate both effectiveness and robustness. Furthermore, we uncover and empirically substantiate a hierarchical generative mechanism for implicit concepts within latent diffusion models—revealing their intrinsic causal organization.

This study addresses the challenge of decoding latent dynamic structures underlying large-scale neuronal population activity by proposing a unified latent variable modeling framework that, for the first time, jointly integrates three core tasks: single-region dynamics modeling, inter-regional communication analysis, and behavioral alignment. The approach combines classical state-space models with cutting-edge deep generative architectures—including Transformers, diffusion models, and neural ordinary differential equations—to systematically construct a taxonomy and establish clear evaluation benchmarks. Emphasizing critical challenges such as causal inference and directional connectivity, this work provides both theoretical foundations and methodological tools for interpretable brain dynamics analysis and robust neural decoding.

This work addresses the challenge of simultaneously ensuring identifiability and extrapolation capability in conditional latent variable models—specifically, how variations in observed attributes shape the latent structure and generalize to unseen attribute values. The authors propose Concept Modulation Models (CMMs), which formalize a generative pathway from attributes through modulators to concepts and ultimately to observations. By introducing an attribute potential function, they unify the characterization of conditional identifiability and extrapolation behavior. The study extends transfer-based identifiability theory to the conditional setting for the first time, establishing a general algebraic criterion that jointly governs identifiability and extrapolation. This framework reproduces and unifies foundational theoretical results from nonlinear independent component analysis and causal representation learning.

This work proposes a probabilistic inference framework that integrates inductive biases to address the challenges of uncertainty quantification in deep sequential models. While traditional Bayesian approaches struggle with prior specification and inference accuracy in large-scale networks, the proposed method establishes a theoretical connection between Transformer attention mechanisms and sparse Gaussian processes, enabling scalable approximate Bayesian inference. It introduces cross-domain inducing points derived from HiPPO operators to support long-range historical modeling in online learning settings. Furthermore, self-supervised signals are leveraged to enrich the probabilistic structure of latent variables in sequence generation. The resulting approach significantly enhances the uncertainty quantification capability, probabilistic expressiveness, and scalability of deep sequential models, all while maintaining competitive predictive performance.

This work addresses the computational bottleneck arising from integrating out individual random effects in sequential latent variable models with heterogeneous subjects. To overcome this challenge, the authors propose the Anchored Variational Expectation-Maximization (AVEM) framework, which evaluates the posterior of local latent processes at representative anchor points of the individual random effects. This approach preserves local tractability while substantially reducing computational complexity. Theoretical analysis shows that the posterior mean constitutes a near-optimal anchor point and guarantees local monotonicity of the variational EM algorithm. A partially anchored variant is further introduced to accommodate varying degrees of posterior concentration. Experiments on mixture hidden Markov models and mixed-effects state-space models demonstrate that AVEM achieves superior parameter estimation accuracy alongside significant gains in computational efficiency.